If the quadratic equation x^2 + 2x + 1 = 0 is solved, what are the roots? (2022)

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Question: If the quadratic equation x^2 + 2x + 1 = 0 is solved, what are the roots? (2022)

Options:

Correct Answer: -1

Exam Year: 2022

Solution:

The equation can be factored as (x + 1)(x + 1) = 0, giving the root -1 with multiplicity 2.

If the quadratic equation x^2 + 2x + 1 = 0 is solved, what are the roots? (2022)

If the quadratic equation x^2 + 2x + 1 = 0 is solved, what are the roots? (2022)

Step 1: Start with the quadratic equation x^2 + 2x + 1 = 0.
Step 2: Identify the coefficients in the equation: a = 1, b = 2, c = 1.
Step 3: Look for two numbers that multiply to 'c' (1) and add to 'b' (2). The numbers are 1 and 1.
Step 4: Rewrite the equation using these numbers: (x + 1)(x + 1) = 0.
Step 5: Set each factor equal to zero: x + 1 = 0.
Step 6: Solve for x: x = -1.
Step 7: Since both factors are the same, the root -1 has a multiplicity of 2.

Quadratic Equations – Understanding how to solve quadratic equations using factoring, the quadratic formula, or completing the square.
Roots and Multiplicity – Identifying the roots of a quadratic equation and understanding the concept of multiplicity in roots.